What is laplacetransform 2sin^2(t) ?

The answer to laplacetransform 2sin^2(t) is 4/(s(s^2+4))

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laplacetransform 2sin^2(t)

laplace transform

2 sin^{2} (t)

\frac{4}{s ( s ^{2} + 4 )}

Solution steps

L {2 sin^{2} (t)}

Rewrite using trig identities

L {1 - cos (2 t)}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {1} - L {cos (2 t)}

L {1} : \frac{1}{s}

L {cos (2 t)} : \frac{s}{s ^{2} + 4}

= \frac{1}{s} - \frac{s}{s ^{2} + 4}

Simplify

\frac{1}{s} - \frac{s}{s ^{2} + 4} : \frac{4}{s ( s ^{2} + 4 )}

= \frac{4}{s ( s ^{2} + 4 )}

What is laplacetransform 2sin^2(t) ?
The answer to laplacetransform 2sin^2(t) is 4/(s(s^2+4))